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555-605 (Medium)|   Geometry|      
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Bunuel
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What is the ratio of the radii of two vessels of equal volumes if the 18 Aug 2015, 02:30
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E
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35% (medium)

Question Stats:

60% (01:17) correct 40% (01:17) wrong based on 129 sessions

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What is the ratio of the radii of two vessels of equal volumes if the first one is hemispherical in shape and the second one is spherical in shape?

A. 1 : 0.5
B. 1 : 2
C. \(\sqrt 2 : 1\)
D. \(\sqrt 3 : 1\)
E. \(\sqrt[3] 2 : 1\)

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E
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What is the ratio of the radii of two vessels of equal volumes if the 18 Aug 2015, 02:42
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Bunuel
What is the ratio of the radii of two vessels of equal volumes if the first one is hemispherical in shape and the second one is spherical in shape?

A. 1 : 0.5
B. 1 : 2
C. \(\sqrt 2 : 1\)
D. \(\sqrt 3 : 1\)
E. \(\sqrt[3] 2 : 1\)

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Volume of hemisphere=Volume of sphere
2/3pie R^3=4/3pie r^3
R^3/r^3=2
R/r=Cube root 2/1
Answer E
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What is the ratio of the radii of two vessels of equal volumes if the 18 Aug 2015, 04:59
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Bunuel
What is the ratio of the radii of two vessels of equal volumes if the first one is hemispherical in shape and the second one is spherical in shape?

A. 1 : 0.5
B. 1 : 2
C. \(\sqrt 2 : 1\)
D. \(\sqrt 3 : 1\)
E. \(\sqrt[3] 2 : 1\)

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Vol sphere = \(\frac{4\pi {r_1}^3}{3}\)

Vol of a hemisphere = 0.5*Volume of a sphere = \(\frac{2\pi {r_2}^3}{3}\)

Thus, per the question, Vol of sphere = volume of hemisphere ---> \(\frac{4\pi {r_1}^3}{3}\) = \(\frac{2\pi {r_2}^3}{3}\) --->\(\frac {r_2}{r_1}\) = \(\sqrt[3] 2 : 1\)

E is the correct answer.
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What is the ratio of the radii of two vessels of equal volumes if the 18 Aug 2015, 21:22
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Bunuel
What is the ratio of the radii of two vessels of equal volumes if the first one is hemispherical in shape and the second one is spherical in shape?

A. 1 : 0.5
B. 1 : 2
C. \(\sqrt 2 : 1\)
D. \(\sqrt 3 : 1\)
E. \(\sqrt[3] 2 : 1\)

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Volume of a Sphere = 4/3 π \(r_1^3\)
Volume of HemiSphere = 2/3 π \(r_2^3\)
Given both are equal
4/3 π \(r_1^3\) = 2/3 π \(r_2^3\)

2\(r_1^3\) = \(r_2^3\)

\(\frac{r_2}{r_1}\)= ? is asked in the question stem

\(\frac{r_2}{r_1}\) = \(\sqrt[3] 2 : 1\)
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What is the ratio of the radii of two vessels of equal volumes if the 08 May 2021, 07:38
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Bunuel
What is the ratio of the radii of two vessels of equal volumes if the first one is hemispherical in shape and the second one is spherical in shape?

A. 1 : 0.5
B. 1 : 2
C. \(\sqrt 2 : 1\)
D. \(\sqrt 3 : 1\)
E. \(\sqrt[3] 2 : 1\)

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Since the two shapes are spherical the formula involves cubes of radius, the answer is likely to contain cube root of radius.
\(\frac{2}{3}\pi*R^3 = \frac{4}{3}\pi*r^3\)
\(\frac{R}{r} = \sqrt[3] 2 : 1\)

Answer E.
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What is the ratio of the radii of two vessels of equal volumes if the 15 May 2023, 22:46
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